The Law of Mutual Interdependence: Ontological Consequences of Finite Computational Resources in the Universe

This paper derives the "Law of Mutual Interdependence" as a necessary logical consequence of universal finitude and the differentiation of existence. Building upon the premise that the universe is a computational system with finite resources (Saito, 2026), we demonstrate that the existence of a "completely closed system" or "isolated entity" is a thermodynamic and categorical impossibility. By integrating Category Theory (Yoneda Lemma), Landauer’s Principle, and a resource-centric reinterpretation of the Uncertainty Principle, we formalize existence not as a collection of independent substances, but as nodal points within a dynamic relational network. We show that the persistence of any system depends on constant interaction and information exchange to avoid computational halt. This work identifies modern civilizational issues as "structural fallacies of isolation" and provides the logical foundation for the "Principle of Mutual Optimization" to be presented in subsequent work.